Allelic frequency estimation in presence of uncertain priors

Abstract

In this paper, we assume that allele frequencies are random variables and follow certain statistical distributions. However, specifying an appropriate informative prior distribution with specific hyperparameters seems to be a major issue. Assuming that prior information varies over some classes of priors, we develop the concept of robust Bayes estimation into the context of allele frequency estimation. We first assume that the region of interest is a single locus and the prior information is represented in terms of a class of Beta distributions, and present explicit forms of the resulting Bayes and robust Bayes estimators. We then extend our results to biallelic k-loci and multi-allelic k-loci cases within the region of interest. We perform a simulation study to measure performance of the proposed robust Bayes estimators against some Bayes estimators associated with specific hyperparameters. The simulations reflect satisfactory performance of the proposed robust Bayes estimators when there is no evidence implying the actual prior distribution.